Abstract
The height function on an abelian variety is addressed via an analogue of Mahler's measure function. It has previously been shown that the measure of a suitable polynomial yields the canonical height function on an elliptic curve; such work is generalised here to demonstrate that the canonical height on a higher-dimensional abelian variety may also be pursued from this viewpoint. Effective formulae which make use of the group law are given for the computation of local measures, and it is shown how these give rise to the construction of Riemann-style integrals on an abelian variety.KeywordsElliptic CurveAbelian VarietyAlgebraic Number FieldLocal HeightMahler MeasureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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